...the mystery seems to be solved thusly:

John shows a slide from the Picard Museum exhibit that links the crystal dodecahedron to one of the 19th century Levin sample cards, the Pitt Rivers Museum card of beads "Traded into Central Africa"

I tried to show the shape of the blobby polyhedron bead on the right by penciling over the facet edges. A mold seam can be seen around the circumference.

All beads show conical holes, with one end hole smaller than the other - just like the 19th century "Vaseline" beads, yes? A molding tong with a conical pin to perforate the soft heated glass? Beads then ground to remove the flashing?

The center bead is the standard cornerless cube.

The blue tint is from the blu-tak I had to use to get the beads to sit on their sides.